The present invention relates in general to mathematical analysis of time series data with respect to damping and decay relaxation effects.
Damping effects govern the behavior of a wide variety of physical systems. Extracting damping characteristics from measured data is a practice utilized in scientific and engineering applications. For example, structural damping effects on how a bridge reacts during an earthquake or when aircraft experience turbulence is important in order to enable creation of better and safer designs. Damping parameter extraction algorithms have been developed using a variety of techniques and continue to be of considerable scientific and engineering importance. The present invention is a contribution to this technology area.
An empirical study usually involves analysis of time series obtained through sensors. A method for analysis of such test data exploiting the use of the Hilbert Transform, is explained in U.S. Pat. No. 5,983,162 to Huang, issued Nov. 9, 1999. Through computer implemented Empirical Mode Decomposition (EMD), such method decomposes a given dataset into a sum of Intrinsic Mode Functions (IMFs). The Hilbert Transform employed in the usual way specifies instantaneous amplitude and frequency behavior as functions of time for each IMF. The foregoing procedure enables time-frequency dependent signal-amplitude analysis (Hilbert-Huang Spectrum).
However, more detailed physical characteristics of time series datasets may be needed than that afforded by signal-amplitude analysis, such as transient decay relaxation rates, or damping characteristics of resonant mode families. Heretofore, only somewhat limited conventional analyses have been available to examine the damping characteristics of a system. It is therefore an important object of the present invention to provide a method that fully utilizes the benefits of an improved analytical technique realized by use of the EMD and Hilbert Transform in order to determine damping characteristics.
In accordance with the present invention the methodology disclosed in the aforementioned U.S. patent to Huang involving analysis of time series data, is expanded into applications such as time-frequency analysis of structural dynamics and structural shock responses involving development of calculation algorithms on time and frequency damping loss factors through which the damping characteristics of a system are evaluated.
As a first step, a time dependent decay rate function is defined for each empirical mode (k). Based on empirical mode decomposition (EMD), a dimensionless quantity as a function of time (t) is then formulated, corresponding to the critical damping ratio, which is one-half the damping loss factor xcex7k(t) at structural resonance. This damping loss factor is then evaluated at given time and instantaneous damped frequency utilizing the Hilbert transform methodology described in the Huang patent hereinbefore referred to. Algorithmic calculation is utilized to quantify and map time-frequency dependent damping loss factors under a full damping spectrum. A root mean square time average of the damping loss factors is then formulated as a function of frequency and averaging time (T) to provide an analysis of the system damping characteristics based on the time series data obtained from single time measurements.